Transmission channels in wireless networks are subject to fading and interference caused by multiple paths crossed by transmitted signals. These effects lead to an information loss which disables the receiver from efficiently decoding the intended information packets. One solution to this problem consists of transmitting the same information through different links presenting different fading characteristics. Consequently, many replicas of the same signal may be available at the receiver. As a result, the receiver can use the replicas that are less affected by the transmission channel to reliably recover the desired messages.
Different diversity techniques may be used for providing many replicas of the same signal by exploiting different degrees of freedom such as time, space and frequency. Time and space diversity techniques are used for example in Multiple-Input Multiple-Output (MIMO) systems. Different replicas of the same signal may be provided using a multiplicity of antennas and/or a plurality of time slots. Frequency diversity is used for example in OFDM systems for providing different replicas using a plurality of orthogonal sub-carriers. Multipath diversity is used for example in Discrete Sequence-Code Division Multiple Access systems (DS-CDMA).
When different diversity techniques are used simultaneously, the global diversity order achieved by the system represents the product of the partial orders obtained by each technique separately. The global diversity order represents the number of independent replicas of original signals that are available at a receiver to decode the transmitted symbols. It characterizes the reliability of the communication system.
Some diversity techniques have significantly impacted the design of many successful communication systems, such as MIMO technologies. The combination of space and time diversity techniques allows increasing the system capacity.
MIMO technologies have been incorporated in several standards such as in wireless LANs (WiMAX IEEE 802.16) or cellular mobile networks (3G and 4G) and are applied in different applications such as cooperative communications involving relay stations equipped with multiple antennas.
One major challenge for MIMO systems is to adapt to increasing demands in terms of data rates for real-time services and applications. Another challenge is to implement low-complexity decoders at the receiver that are capable of offering the required quality of service while consuming low power and low computational resources.
A receiver device implements a decoding algorithm which delivers an estimation of the conveyed signal from the transmitter.
Several decoding algorithms exist and their practical use differs depending on the performance required in the quality of service (QoS) specifications and the available hardware resources, such as the computational and memory (storage) supplies. Optimal performances in terms of error rate and achievable diversity order can be obtained using a Maximum Likelihood (ML) decoding algorithm. The optimal achievable diversity order designates the maximum global diversity order offered by the communication system. Exemplary ML decoding algorithms include sequential lattice decoders such as:                the Sphere Decoder disclosed in “E. Viterbo and J. Boutros. A universal lattice code decoder for fading channels. IEEE Transactions on Information Theory, 45(5):1639-1642, July 1999.”        the Stack decoder disclosed in “R. Fano. A heuristic discussion of probabilistic decoding. IEEE Transactions on Information Theory, 9(2):64-74, 1963”, and        the SB-Stack decoder disclosed in “G. R. Ben-Othman, R. Ouertani, and A. Salah. The spherical bound stack decoder. In Proceedings of International Conference on Wireless and Mobile Computing, pages 322-327, October 2008”.        
However, these decoders require a high computational complexity which can exceed the available resource. The complexity of sequential ML decoders increases as a function of:                the number of deployed antennas at the transmitter and at the receiver, and        the size of the constellations.        
Sub-optimal decoders were also proposed with a reduced decoding complexity such as linear decoders including Zero-Forcing (ZF) and Minimum Mean Squared Error (MMSE) and non-linear Zero Forcing-Decision Feedback Equalizer (ZF-DFE) decoders. Although they require reasonable computational capabilities, these decoding algorithms offer limited performance and do not allow fully exploiting the full diversity offered by the communication system. Preprocessing techniques such as Lattice reduction and MMSE-GDFE preprocessing may be applied prior to decoding using such approaches to obtain better performance. An example of lattice reduction techniques is the LLL reduction disclosed in: “A. K. Lenstra, H. W. Lenstra, and L. Lovasz. Factoring Polynomials with Rational Coefficients. Math. Ann. Volume 261, pages 515-534, 1982”.
A category of sub-block decoders exists. It refers to decoding approaches consisting in dividing the vector of information symbols into sub-vectors and decoding each sub-vector separately given a sub-block division of a representative channel state matrix and a corresponding sub-vector division of the received signal.
A sub-block decoder was disclosed in “Won-Joon Choi, R. Negi, and J. M. Cioffi. Combined ML and DFE decoding for the V-BLAST system. IEEE International Conference on Communications. Volume 3, pages 1243-1248, 2000”. This decoder is based on a combined decoding scheme using both ML and DFE. According to this approach, the vector of information symbols of length n is divided into two sub-vectors of lengths p and n-p respectively. In a first decoding phase, the sub-vector composed of p information symbols is estimated using an ML decoder. Given these estimated symbols, the receiver iteratively performs inter-symbols interference cancellation using a decision feedback equalization to determine an estimation of the remaining n-p symbols composing the second sub-block of information symbols. Such a decoding scheme provides better performances than a joint decoding based on a ZF-DFE decoder. For example, the diversity order achievable under this scheme in a symmetric MIMO system using spatial multiplexing is equal to p while it is limited to 1 under ZF-DFE decoding.
Other sub-block decoding schemes have been proposed for Space-Time Coded MIMO systems using a linear Space-Time Block Code (STBC). Particular classes of low-complexity ML decodable STBC have been proposed such as the family of multi-group decodable codes disclosed in:                “D. N. Dao, C. Yuen, C. Tellambura, Y. L. Guan, and T. T. Tjhung. Four-group decodable space-time block codes. IEEE Transactions on Signal Processing, 56(1):424-430, January 2008”.        “T. P. Ren, Y. L. Guan, C. Yuen, E. Gunawan, and E. Y. Zhang. Group-decodable space-time block codes with code rate >1. IEEE Transactions on Communications, 59(4):987-997, April 2011”.        
Other classes of low-complexity ML decodable STBC comprise fast decodable codes disclosed in:                “E. Biglieri, Y. Hong, and E. Viterbo. On fast-decodable space-time block codes. In IEEE International Zurich Seminar on Communications, pages 116-119, March 2008”.        “J. M. Paredes, A. B. Gershman, and M. Gharavi-Alkhansari. A new full-rate full-diversity space-time block code with nonvanishing determinants and simplified maximum-likelihood decoding. Signal Processing, IEEE Transactions on, 56(6):2461-2469, June 2008”.        
Another family of STBC codes referred to as “fast-group decodable codes” was disclosed in T. P. Ren, Y. L. Guan, C. Yuen, and R. J. Shen. Fast-group-decodable space-time block code. In Proceedings of IEEE Information Theory Workshop, pages 1-5, January 2010”.
Sub-block decoding in the presence of an STBC that belongs to one of these families of codes may be advantageously performed using the QR decomposition of the channel state matrix. Accordingly, the zero structure of the equivalently obtained transmission channel representative matrix allows recursive decoding of the various sub-vectors of information symbols with reduced complexity without sacrificing the decoding error performance. Particularly, some sub-vectors of symbols may be estimated in a separately in parallel allowing for faster and lower-complexity decoding. Different or similar decoding schemes may be used to determine each estimate of the sub-vector of information symbols.
Although existing sub-block decoding methods offer better performance than sub-optimal linear and non-linear decoding schemes, they require higher computational complexity.